**Lie Group Analysis of Unsteady Flow of Kerosene**/**Cobalt Ferrofluid Past A Radiated Stretching Surface with Navier Slip and Convective Heating**

### **Hossam A. Nabwey 1,2,\*, Waqar A. Khan 3 and Ahmed M. Rashad 4**


Received: 29 April 2020; Accepted: 17 May 2020; Published: 19 May 2020

**Abstract:** In this work, we identified the characteristics of unsteady magnetohydrodynamic (MHD) flow of ferrofluid past a radiated stretching surface. Cobalt–kerosene ferrofluid is considered and the impacts of Navier slip and convective heating are additionally considered. The mathematical model which describes the problem was built from some partial differential equations and then converted to self-similar equations with the assistance of the Lie group method; after that, the mathematical model was solved numerically with the aid of Runge–Kutta–Fehlberg method. Graphical representations were used to exemplify the impact of influential parameters on dimensionless velocity and temperature profiles; the obtained results for the skin friction coefficient and Nusselt number were also examined graphically. It was demonstrated that the magnetic field, Navier slip, and solid volume fraction of ferroparticles tended to reduce the dimensionless velocity, while the radiation parameter and Biot number had no effects on the dimensionless velocity. Moreover, the magnetic field and solid volume fraction increase skin friction whereas Navier slip reduces the skin friction. Furthermore, the Navier slip and magnetic field reduce the Nusselt number, whereas solid volume fraction of ferroparticles, convective heating, and radiation parameters help in increasing the Nusselt number.

**Keywords:** MHD; ferrofluid; Lie group framework; unsteady slip flow; stretching surface; thermal radiation
